Solve the system of equations: $$\frac{15x-3y}{4} + \frac{3x+2y}{6} = 3$$ $$\frac{3x+y}{3} - \frac{x-3y}{2} = 6$$

Multiply the first equation by 12 and the second by 6 to eliminate denominators:
1) $$3(15x-3y) + 2(3x+2y) = 36 \implies 45x - 9y + 6x + 4y = 36 \implies 51x - 5y = 36$$
2) $$2(3x+y) - 3(x-3y) = 36 \implies 6x + 2y - 3x + 9y = 36 \implies 3x + 11y = 36$$
Multiply the second simplified equation by 17: $$51x + 187y = 612$$
Subtract the first simplified equation from this new equation: $$(51x + 187y) - (51x - 5y) = 612 - 36 \implies 192y = 576 \implies y = 3$$
Substitute $$y=3$$ into $$3x + 11y = 36$$: $$3x + 11(3) = 36 \implies 3x + 33 = 36 \implies 3x = 3 \implies x = 1$$
The solution is $$x=1, y=3$$.